Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
366 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 366 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #26041981 | C2 | semidirect |
| 2. #26041680 | C2 | semidirect |
| 3. #26041601 | C2 | semidirect |
| 4. #26041595 | C2 | semidirect |
| 5. #26041577 | C2 | semidirect |
| 6. #26041512 | C2 | semidirect |
| 7. D8×Dic181 | C2 | semidirect |
| 8. C8×C22⋊D181 | C2 | semidirect |
| 9. #26041316 | C2 | semidirect |
| 10. C2×#19153750 | C2 | semidirect |
| 11. #466×C181 | C2 | semidirect |
| 120. C181 | #3339 | semidirect |
| 128. #466 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041981 | 2 |
| #26041680 | 2 |
| #26041601 | 2 |
| #26041595 | 2 |
| #26041577 | 2 |
| #26041512 | 2 |
| D8×Dic181 | 2 |
| C8×C22⋊D181 | 2 |
| #26041316 | 2 |
| C2×#19153750 | 2 |
| #466×C181 | 2 |
| #3339 | 181 |